Anti-aircraft gun computer



Seggi. M

, 3956 E. E. LEMAN ET AL ANTI-AIRCRAFT GUN COMPUTER 5 Sheets-Sheet lFiled June 5 ACTUAL VELC/TY 0555/?!/59 DATA VELC/TY TARGE ACTUAL PATHNORTH w M m s w R X M U M x0 n JN VEN TORS. E Ljbznan,

pi?, E956 E. E. LEMAN ETAL 2,752,555

ANTIIRCRAFT GUN COMPUTER Filed June 5, 1950 3 Sheets-Sheet 2 NINVENTORS. s MEL/ibm ANTI-AIRCRAFT GUN CGNIPUTER Earl E. Libman,Brooklyn, Aaron D. Fialkow, New York,

Sohn W. Bozeman, Baidwin, and irving Gerst, Brookiyn, N. Y., assignorsto Contro instrument Company, Zinc., Brooklyn, N. Y., a corporation ofNew York Application June 5, 1950, Serial No. 166,192

13 Claims. (Cl. 23S-61.5)

ri`his invention relates to computers and has particular reference to asystem for computing a forecast of the future position of a movingtarget and of the direction in which a projectile should be launched sothat it will hit that target.

In computers or' this nature, the computation of future target positioncustomarily proceeds on the assumption that the target will continue tomove from the position it occupies at the moment of projectile launchingwith the instantaneous velocity and direction it has at said moment, andthat the data of instantaneous position, Velocity and direction of thetarget given by a tracking mechanism is adequate. However, the data thusobtained does not necessarily represent the true position, velocity anddirection of the target.

Therefore, in accordance with the present invention and in order toobtain a more accurate forecast of future target position, thecomputation of such position, while it proceeds on the rst of the abovementioned assumptions that the target will continue to move with thevelocity and direction it has at the instant of tiring a projectilethereat, further utilizes computed values of target velocity anddirection that are obtained by operating upon data received from atracking mechanism over a period of time just preceding the launching ofsaid projectile.

The above rand other objects of the invention will be made apparent fromthe following description and drawings which illustrate a preferredembodiment of the inventive idea.

ln the drawings:

Fig. l is a diagram representing the observed data of a targets path,the actual path of the target, and the errors distinguishing these pathsfrom each other;

Fig. 2 is a diagram representing the coordinate axes to which thecomputation is referred;

Fig. 3 is a diagram showing the time history of one of the observedcoordinates of the target path and of the corresponding coordinate ofthe least squares path, to be hereinafter dened, along with the varioussymbols used in the computation;

Fig. 4 is a diagrammatic view illustrating the components which comprisea preferred embodiment of the invention; and

Fig. 5 is an enlarged fragmentary plan view of a voltage recordingmechanism shown in Fig. 4.

General principles When a tracking mechanism follows a moving target, itoscillates or hunts about its position, and the data furnished by saidmechanism contains errors, and even if the data of position deviatesfrom that targets true position in small measure so that the positionaldata obtained therefrom can be considered to be quite accurate, thevelocity data, especially with reference to direction, may be enormouslyin error. As illustrated in Fig. l, the positional error shown at Cconstantly varies, but, if the tracking device is an accurate one, theposition indicated will always be in the immediate neighborhood of theactual position of the target. However, the observed data at the instantof tiring indicates a movement of the target toward B which is differentfrom the actual direction of motion of the target toward A. Hence,although the error in position may be very small, the error in directionmay, nevertheless, be large, as indicated by the angle D.

in order to make a forecast of the future position of the target (basedon the assumptions previously indicated) so that a projectile can betired to hit the same, it is necessary to know the target position,velocity and direction at the instant said projectile is launchedthereat, and a means to make an accurate determination of thesequantities is essential. To make such a determination, all that isavailable is a continuous record of observations of target behavior.From this, by the means hereinafter shown, a path can be determinedwhich closely approximates the true path taken by the target and fromwhich may be determined the direction and velocity information requiredto launch a projectile at said target in order to hit the same.

Of the methods suited to operate upon the observed, data of the targetpath to obtain a close approximation to the true targets path during theimmediate past, and from which the velocity and direction of the targetat the instant of projectile launching may be computed, the method andunderlying theory utilized in this invention will now be described.

lt is shown in the theory of probability that, from a series ofobservations in which the errors of observation constitute a normalprobability distribution, the most probable value of the observedquantity results from the application of the method of least squares. inthe present invention, these statistical considerations are applied tothe observed path of the target to determine the most probable targetpath during a time interval in the immediate past.

The targets actual motion during the immediate past can be closelyrepresented by the following set of parametric equations:

where the As, Bs and Cs are literal coethcients to be determined, by theapplication of the method of least squares, from the observed data, andt is time measured from some arbitary initial instant. indeed, forpractical military iiights, the above set of equations, with 11:3, issuicient to closely represent the targets history over a suthcientlysmall period of time, for n=3 is the lowest degree for which the setrepresents a three-dimensional curve whose curvature and torsion at anypoint may assume any values. The equations are thus In order todetermine the coeiiicients by the method of least squares, it isnecessary that these values be such that the sum of the squares of thedistances at each instant, during a fixed time interval in the immediatepast, between the path represented by the equations (which will becalled the least squares path) and that represented by the observeddata, be a minimum. This may be accomplished by utilizing themathematical expression for the distance between the observed positionof the target at any time and the corresponding point (at that time) onthe least squares path. The observed position is known and theexpression for the position on the least squares path contains theunspecified coeicients. Thus an expression may be obtained for thesquare of that distance agreaeee and by adding together all suchexpressions during some known interval just prior to ring there isobtained a summation which contains the unspecified coefficients. Bywell lgnown methods ot` mathematics, the coefficients may then be sodetermined that this sum is a minimum. This determination gives theequation of the most probable target path of the type indicated whichcan be obtained from the observed data.

By mathematical differentiation of the equation of the least squarespath, the present target velocity vector is obtained. Then, byextrapolating along that vector for a distance equal to its magnitudemultiplied by the time of projectile flight, the advance position of thetarget is obtained. The usual methods of ballistics may then be used toconvert this advance position to the orders required to position theprojectile launching device.

Mathematical analysis Consider the horizontal plane through the presentgun position. Choose a set of axes through the gun position such thatthe positive directions of the axes of x, y and z point North, East andUp, respectively, as shown in Fig. 2. The target at the present instant2:11, has the following polar coordinates: present compass bearingpresent elevation above the horizontal e and present range R. These arethe observable data which are usually obtained from the sightingmechanism.

Let x, y and z represent the corresponding rectangular coordinates ofthe target. Then, if r is the projection of R on a horizontal plane,

Since these are computed from the observed polar coordinates, they maybe termed the observed rectanguiar coordinates.

The following analysis will be carried out for x alone. The analysis fory and for z is exactly similar and reed not be repeated.

As shown in Fig. 3, which iigure is a plot of the variations i x withrespect to time, the diterence at any in stant t between the observed xcoordinate and the corresponding X coordinate of the least squares pathis X( t) -x(t). The sum of the squares of these differences over anarbitrary period of 2q seconds just prior to the present instant t=p isequal to the integral The most probable value of the X-coordinate at agiven time D is determined by selecting values for the coefcients Au,A1. Az and As in Equations l such that t=pe2q The velocity of :t targetflying along the least squares path at instant t is XU) where X(t) isintended to mean dX(t) dt [X(t) x(tWdt--minimum is used, so that theprojectile is actually directed to hit the point whose x-coordinate isThe targets least'squares path is given by Equations l.

if, for convenience, time is measured from an arbitrarily chosen instantq seconds prior to the present instant and this time is indicated by thevariable s, there is obtained, by substituting t=pq+s (Fig. 3) inEquations l, the following expression for XU) and, of course, similarexpressions for )'(t) and Z(t),

where the as are functions of p and q.

Similar substitution in equation 4 gives:

The values of the as that make the integral a minimum are, by the wellknown methods of calculus:

Fhrt-5K2] known by Equations 9, and from Equations 8 all of the as areknown and, therefore, the coecients in the Equation 6 for the Xcoordinate of the least squares path are now known. Differentiation ofEquation 6 with respect to t gives and so by Equation 5, xA is known.

Following an analogous process for Y and Z, YA and ZA are obtained whichgive the rectangular coordinates of the advanced point at which theprojectile is launched to obtain a hit. By converting these back intopolar coordinates, the data, after ballistic corrections, for trainingand elevating a gun or other projectile launching apparatus, and therange for which the fuse of the projectile should be set, are known.

The computer ln actual practice, target range, elevation and bearing maybe obtained from a tracking device such as a radar, or an optical sightand range nder. The elevation and bearing thus obtained will beavailable, mechanically, as angular displacements from the axes of thetracking device. From a radar, the range will be available as a arcanesA voltage; and from an optical range finder, as a mechanical angulardisplacement which may be converted to a voltage.

The voltage representing range is introduced into the computer by way ofthe leads 5 and 6 (Fig. 4) thus energizing the rotor 7 of the resolver8, which rotor is positionable by means of 'the shaft 9 with respect tothe mutually perpendicular stator coils 10 and 11. The Shaft of theresolver 8 is positioned by the mechanical input of target elevationand, therefore, the voltage induced from the rotor into the stator coilswill be, respectively,

R sin e=z, and

R cos e=r which outputs are respectively on the leads 12, 13 and 14, 15.

The voltage on leads 14 and 15, proportional to r, is

introduced into the rotor 16 of the resolver 17 which is similar inconstruction to the resolver 8 and whose shaft 18 receives themechanical input of target bearing and positions the rotor 16. Thevoltages then induced in the stator windings 19 and 2l) are r sin =y andr cos =x Thus, there is obtained the rectangular coordinates x, y and zof the targets present position.

Since the subsequent operations performed by the computer are the samefor each of the coordinates x, y and z it will be suicient, as before,to trace the operations performed upon the x coordinate alone, it beingunderstood that similar treatment is accorded the y and z coordinatedata before they are recombined finally at the output.

To the voltage representing the instantaneous value of x from leads 23and 24, is added a biasing voltage of magnitude (L-B) by placing thesecondary 59 of transformer 57 in series between leads 24 and 24a, whereL is the window width and B is a quantity of maggnitude greater than themaximum negative value of x and is such that L-(B-l-x) and B-l-x arealways positive. The alternating voltage on the primary 58 oftransformer 57 is supplied by leads 28 and 29 from the same source asthat supplied to leads 5 and 6 of resolver B.

The voltage L-(B-t-x) actuates the galvanometer and causes its pen 30 totrace an opaque area 31 on a transparent surface or ribbon 32 of widthL-(B-l-x). Since the window 39 in the mask 39' directly above thesurface 32 is of width L, there is then left a transparent portion whosewidth is B-l-x. The ribbon 32 is carried by the rollers 33 and 34 and isof sucient width to accommodate without overlapping the three tracesmade by the galvanometers 25, 26 and 27. The roller 34 is driven underthe window 39, whose length is two inches, at the rate inches per secondby means of the gears 35 and 36, the speed selector 37 into which q isset, and the time motor 38. This quantity q, which is arbitrarilychosen, may be of the order of seconds, and is introduced by means ofthe hand wheel 40, which turns the shaft 41 whose threaded portion 42causes the traveling nut 43 to vary the position of the elements of theselector 37, and thus the speed of the drive to roller 34.

Since the ribbon 32 is running at a speed of inches per second, the timeit requires to move two inches is 2q, so that the window 39 covers thesampling time 2q.

By Figs. 3 and 5, s is time measured from the midpoint of the samplingtime interval 2q, and the ribbon running at the speed moves relative tothe midpoint of the window and in the time s will move the distance Qwhich, by Equation l0 is w. Therefore, it follows from Figs. 3 and 5that w measures the distance along the window 39 from the midpoint tothe point on the said ribbon corresponding to the instant t.

ln the time dt. the strip moves a distance La q which equals dw fromEquation l() (Fig. 5). In an elementary piece of the ribbon at distancew from the center line of the window and of width dw, the transparentarea is (B+x).dw.

A light source 44 is energized by way of the leads 45 and 46. This lightsource must be of constant intensity. Of the various ways for obtainingsuch constancy the following is given as an illustration. The lenssystem 47 focuses the light upon the photocell 48 that controls theactivity of the amplifier 49, which amplifier controls the powerdelivered to the light source. This arrangement causes the powerdelivered to said source to vary in such a Way as to maintain itsbrightness constant. In order to electrically manipulate the computingdevices receiv ing the light after transmission through the ribbon 32,it is desired that the light be modulated with the line frequency. Thefollowing is given as an illustration of one way to secure thisdesideratum.

A lens system 5l) causes a part of the light from the source to becolumnated and these parallel rays are transmitted through three sets ofpolarizing filters 5l and associated polarizing cells 52, said setsbeing angularly disposed relative to each other about the light source44 and each being individual to one of the coordinates x, y and z. Twoof said sets direct their rays, respectively, to the mirrors S3 and 53band thence to the windows 39 and 3971 while the rays from the third setare transmitted directly to the window 39a. Each polarizing cell isactivated by connection to leads 23 and 29 so that the lighttherethrough changes its plane of polarization at line frequency, andthe combined filter 51 and cell 52 of each set therefore modulates theparallel rays in intensity at the rate at which the cell 52 is caused tochange its plane of polarization. The parallel rays emanating from thethree lens systems are thus caused to pass through the windows 39, 39a`and 39b to the associated mirrors 55, 55a and SSb of the three opticalsystems shown; and since the computations for the coordinates x, y and zare effected in the same manner, the following detailed description willbe confined to the optical system obtaining its light through the window39.

The amount of light coming through this window will be determined by thetransparent area which. in turn, is the entire window area diminished bythe opaque portion written into that area by the galvanometer pen 30. Ithas been shown that the light through the narrow ribbon of width dw(Fig. 4) -is (B+x)dw and Ithus the light through the entire window is(12) V21 [B+x1dw This light is caused to fall on the mirror 55, whichmirror is so constituted as to permit 3%; of the light incident thereonto be transmitted therethrough and the remaining A to be rellectedtherefrom. The reflected light passes through the uniform filter andfalls on a photoelectric cell 56. The voltage produced thereby isproportional to the integral (12). This integral is, by Equation 9,

which is the entire light falling on photocell 56 and is therefore thevoltage output of amplifier 61.

The remainder of the light, which was transmitted through the mirror 55,falls upon the mirror 62, which mirror is similar to the mirror 55 inthat part of the light incident thereupon is transmitted and theremainder is reflected. One-third of the light incident upon the mirror62 is reflected therefrom. That passing through the ribbon of width dwat distance w from the window midpoint point is, as before, proportionalto (B-i-x) dw which light then passes through the filter 63 whosetransmission varies along its vertical length, so that at a pointdistance w from its midpoint it transmits the fraction l/2 (1+w) of thelight falling upon it. Since w lies in value between +1 and 1, itfollows that /2(1lw) is always positive and not greater than l. Thus thelight (B+x)dw from the ribbon of width dw, after passing through thefilter. is 1/z(l+w)(B-lx)dw, and the entire light through filter 63 is,by Equation 9.

which is the entire light that falls upon the photocell 64 and thevoltage output of amplifier 65 is Kr-l-(Ko-l-ZB). The remainingtwo-thirds of the light transmitted through the mirror 62 is incidentupon the mirror 66 which, like the foregoing mirrors, transmits one partand reects another part of the light incident thereon. Onehalf of thelight incident thereon is reflected and passes through a tilter 67 whosetransmission, at a point distance w from its midpoint, is the factor wzof the incident light so that the entire light falling on the photocell68 is proportional to .V +1 J-i by Equation 9. This is,` therefore, theoutput of amplitier 69.

The remainder of the light transmitted through the mirror 66 causes theimage in the window 59 to fall upon the filter 70 whose transmission atany point distance w from the midpoint is the fraction 1/:(l,'-w3) ofthe incident light so that the entire light falling on photocell 71 isby Equation 9. Thus. the output of amplier 72 is Ka-l-(Ko--2B).

The transformer 57 has two additional windings 73 and 74, the winding 74yielding a voltage 2B and the winding 73 appears on its secondary 80.

The output voltage Kol-2B of amplifier 61 in opposition series with theoutput voltage Ki-l-(Kol-ZB) of amplifier 65, puts voltage K3 across theprimary 34 of transformer 85. This transformer having a 1:2 windingratio yields on its secondary 86 the voltage 2Ki.

The output voltage X24-36B of amplifier 69 in opposition series with theoutput voltage 6B of the secondary 73 puts voltage K2 across the primary91 of transformer 90. This transformer having a 4:3 Winding ratio, thevoltage fKz appears on its secondary 92.

The output voltage Ka-i-(Ko-I-ZB) of amplifier 72 in opposition serieswith the output voltage Kn-l-ZZB of amplier 61 puts voltage K3 acrossthe primary 94 of transformer 95. This transformer having a 2:7 windingratio yields on its secondary 96 the voltage 7/2K3.

By means of the leads 99, the secondaries 96, 92, 86 and are placed inseries so that the voltage which appears across the leads 23 and 101 isequal to K [-f-zKmLKnLgtnl This expression is multipled by by means ofthe shaft `41, the gears 102 and the cam 103, whose cam surface has forits generating expression and is driven bythe shaft 4l.

The follower 104 whose position is then proportional to carries thesliding Contact 195 of a potentiometer 106 which is joined at its endsto the leads 23 and 101. The voltage from the tap 107 to the lead 23`vill therefore be the voltage across the entire potentiometermultiplied by the factor i. e., giving This voltage is then multipliedby the time of ight T, as required by Equation 5. giving TX(p) by meansof the positionable tap 11,28 of potentiometer 169 which connects thetap 107 to lead 23. The position of tap 108 is made proportional to timeof flight T by being driven by the traveling nut on the shaft 110 which,by means ofthe gears 111, 112, 113, 114 and the shafts 115, 116, 117, isturned proportionally to T by the output shaft 118 of the time of flightcomputer 119 which may be of a construction similar to that shown in U.S. Patent 2,403,543, dated Iuly 9, i946.

The voltage thus obtained across leads 121 and 122 is TX(p) and this, inseries with the voltage x available from the resolver 17 on the leads 23and 24, yields the sum T'p) +x(p) which, by Equation 5, is xa which isthe rectangular cordinate of the target position at the time T in thefuture.

The mechanism above described for the computation of x is duplicated inFig. 4 for y and z which are converted into Ya and Za, and like numeralsare employed to designate similar parts with the addition to saidnumerals of the subscripts a and b denoting the different portions ofthe mechanism for the computation of y and z. respectively.

The voltages represented by xt. ya and za are amplied. respectively, inthe amplifiers 123, 124 and 125. The amplified voltages representativeof xa and ya are combined in the combining mechanism 126 which has twoeld coils 127 and 12S so arranged as to have their respective fields atright angles to each other. The rotor 129 has two coils 130 and 131andthe voltage induced in said rotor is amplified in amplifier 132 andused to excite the motor 133 to drive the shaft 134 which positions saidrotlor. if any voltage is induced in the coil 130, the motor will beenergized and will continue to drive the shaft 134 until said coil is sopositioned that the voltage induced therein is zero; that is to say, itis parallel to the resultant field produced by xa and ya. The coil 131will therefore be at right angles thereto and have an output voltageproportional to this resultant field which from equations similar to(2), but with subscripts a, corresponds to ra and the position of theshaft 134 by the same equations will be proportional to the advancebearlng a The Voltage proportional to ra on coil 131 is amplified in theamplifier 135 and energizes winding 136 of the combining mechanism 137whose remaining winding 138 .is energized by za. In the same way as forthe element 126, the winding 139 whose output is amplified in theamplifier 140 will drive the motor 141 which in turn will position therotor 142 until the coil 139 has no voltage induced therein. Theposition of the shaft 143, which is coupled by means of the gears 144and shaft 145 to the motor 141, will therefore represent es and theoutput of the coil 146, the advance range Re to the target.

The advance target range Ra. is amplified in amplier 147 and is used toposition a servomotor 148 making this range available as adisplacementby means of gears 149 on the shaft 150.

The time of projectile flight is a function of the advance target rangeand elevation. Since this is a function of two variables, athree-dimensional cam is generally employed, although this is not theonly method available, to compute the time of projectile flight fromsuch data. The mechanism 119 represents such a time of iiight computerwhich may employ any of the well known methods of taking into accountsuch characteristics and when operated by range Ra, as supplied byservomotor 148, by way of shafts 151 and 152 and gears 153, and advanceelevation by way of shafts 145, 154 and gears 155, it Will compute thetime of ght for the projectile so that it may be launched on a collisiontrajectory. The tiene of ilight thus computed is the time of iiig'ntwhich, by way of shaft 118, gears 114, etc., is introduced into thecomputation of the coordinates on shaft 119 to position the variabletaps of potentiometers 109, 109a and 109b.

To avoid complicating the drawings with mechanisms old in the art, nomeans are shown for the usual corrections required in ballistics forwind velocity, change in projectile launching velocity, supereievationand the like. Means to accomplish these functions may be driven by theoutputs of future target coordinates as they are produced by themechanism disclosed, and the manner of their accomplishment isimmaterial to the manner in which these future target coordinates areevolved.

The realization of the gun positions by the use of the principlesdescribed above to the known positions occupied by the target may beaccomplished by means other than those specifically disclosed herein.The required integrations might, for example, be performed by ball andtable integrators and the required multiplications, divisions, additionsand subtractions by means of linkages, potentiometers or other meansknown to the computing art. The embodiment herein shown and described,together with the method of computation, constitutes the invention, andsaid embodiment is intended merely to illus trate rather than to limitanddene the mode of realization and scope of the invention, referencebeing had to the appended claims for that purpose.

What is claimed is:

1. An apparatus for computing the direction in which a projectilelaunching device must point in order that a projectile launchedtherefrom will score a hit on a moving target, said apparatus comprisinginput means for the observed spherical coordinates of target position,computing means coacting with said input means for continuouslydetermining, by computations eected by said computing means anddepending upon the coordinates of every observed position that thetarget occupies during an arbitrary interval in the immediate past, themost probable actual path being followed by said target and the velocityof said target in said most probable path, said computing meansincluding, in combination, means responsive to said input means forresolving said observed data of every target position into rectangularcoordinates, means for forming a continuous record of each of saidrectangular coordinates of target position so resolved, means forsensing the entire record of each of said recorded rectangularcoordinates of target positions as recorded over said arbitrary intervalin the immediate past, optical means including a system of associatedlight reflectors and filter elements coacting with said sensing means,means responsive to said optical means for converting each of saidsensed records to yield one component of the velocity of the target insaid most probable path, means to utilize the components thus obtainedfor extrapolating along the line parallel to the tangent ot' said mostprobable path and through the observed position of the target at theinstant of projectile launching to determine a point whose distancealong said tangent from said observed target position at said instant isthe product of the time of projectile iiight and of the velocity of saidtarget in said computed path, means for computing the projectile time ofight, and means to convert the coordinates of said extrapolated pointinto range and angles of train and elevation for the projectilelaunching device.

2. An apparatus for computing the direction in' which a projectilelaunching device must point in order that a projectile launchedtherefrom will score a hit on a moving target, said apparatus comprisinginput means for the observed spherical coordinates of target position,computing means coacting with said input means to continuouslydetermine, by computations depending upon the coordinates of everyobserved position that the target occupies during an arbitrary intervalin the immediate past, the most probable path of said target during saidinterval, said computing means including, in combination, meansresponsive to said input means for resolving said observed data of everytarget position into rectangular coordinates, means for forming acontinuous record of each of said rectangular coordinates of targetposition so resolved, photometric means including coacting light filtersand photo cells for sensing the entire record of each of said recordedrectangular coordinates of target positions as recorded over said pastarbitrary interval, optical means including a system of associated lightreilectors and filtering elements coacting with said sensing means,means responsive to said optical means for converting each of saidsensed records to yield one component of the velocity of the target insaid most probable path, means to utilize the components, thus obtainedfor extrapolating along the line parallel to the tangent of said mostprobable path and through the observed position of the target at theinstant of projectile launching to determine a point whose distancealong said tangent from said observed target position at said instant isthe product of the time of projectile ight and of the velocity of saidtarget in said computed path, means for computing the projectile time offlight, and means to convert the coordinates of said extrapolated pointinto range and angles of train and elevation for the projectilelaunching device.

3. The method of computing the most probable advanced coordinates of atargets position at a time of flight T in the future, which methodconsists in continuously observing and recording the observedinstantaneous coordinates (x, y, Z) of a targets position, deterspaanse"i1 A l'. mining the Values of the coetflcients At, Bt, Cl (1:1, 2. n)of a computed curve of the form so that said curve best represents theactual positions of the target, determining from the computed curve theinstantaneous rate of change of target position X, Y, Z on that curveand extrapolating at the determined rate of change and for the time Talong a line through the observed target position at the present instantand parallel to the tangent to the computed curve at that instant toobtain the most probable target coordinates at said time of ight in thefuture. r'

4. The method of computing the most probable advanced coordinates of atarget position at a time of ight T in the future which consists incontinuously observing and recording7 the instantaneous observedcoordinates (x, y, z) of a targets position, determining the values ofthe coeticients At, B1, Ct (i=l, 2, n) of a computed curve of the formso that the sum of the squares of the differences between thecoordinates represented by said computed curve at any instant and thecorresponding coordinates of the observed target position at thatinstant over an arbitrary interval of time in the immediate past is aminimum,` determining from the computed curve the instantaneous rate ofchange of target position along that curve, and extrapolating at thedetermined rate of change and for the time T along a line through theobserved target position at the present instant andparaliel to thetangent to the computed curve at that instant to obtain the mostprobable target coordinates at said time of flight in the future.

5. The method of computing the most probable advanced coordinates of atarvets position at a time of flight T in the future which consists incontinuously observing and recording the observed instantaneouscoordinates (x, y, z) of a targets position, determining the values ofthe coefficients Ai, Bt, Ct (z'=1, 2, n) of a computed curve of the formso that the sum of the squares of the differences between thecoordinates represented by said computed curve at any instant and thecorresponding coordinates of the observed target position at thatinstant over an arbitrary interval of time in the immediate past is aminimum with the value of n being restricted to n3, determining from thecomputed curve the instantaneous rate of change of target position alongthat curve, and extrapolating at the determined rate of change and forthe time T along' a line through the observed target position at thepresent instant and parallel to the tangent to the computed curve atthat instant to obtain the most probable target coordinates at said timeof ight in the future.

6. The method of computing the most probable advanced coordinates of atarget position at a time of tiight T in the future which consists incontinuously observing and recording the instantaneous observedcoordinates tr. y, z) of a targets position; determining the values ofthe coefficients At, Bt. Ci (1:1, 2, computed curve of the form .11)cfa" so that the sum of the squares of the differences between thecoordinates representedtby said curve at any instant and thecorresponding coordinates of the observed target position at thatinstant over an arbitrary interval of time inthe immediate past is aminimum with the value of n being restricted to n-3, determining fromthe computed curve the instantaneous rate of change of X, Y, Z andconsidering the same to be the target velocity at that instant, andextrapolating at the determined rate of change and for the time T alonga line through the observed target position at the present instant andparallel to the tangent to the computed curve at that instant to obtainthe most probable target coordinates at said time of flight in thefuture.

7. An apparatus for computing the direction in which a projectilelaunching device must point in order that a projectile launchedtherefrom will score a hit on a moving target, said apparatus comprisinginput means for the observed data of target position, computing meanscoacting with said input means for continuously determining, bycomputations depending upon the coordinates of every observed positionthat the target occupies during an arbitrary interval in the inmediatepast, the most probable path of said target during said interval, saidcomputing means including, in combination, means responsive to saidinput means for resolving said observed data into rectangularcoordinates, means to form a continuous record of each coordinate,photometric means for simultaneously sensing the entire records of allsaid coordinates during said past arbitrary interval, optical meansincluding a system of associated light retlcctors and tiltering elementscoacting with said sensing means, said light reilectors each reflectinga portion of the light from said sensed records, a plurality oftransformers having windings connected to said optical means forconverting said sensed records to yield the various components of targetvelocity in said most probable path, means connected to saidtransformers for utilizing said various components to extrapolate alonga line parallel to the tangent of said most probable path and throughthe observed position of the target at the instant of projectilelaunching to determine a point whose distance along said tangent fromsaid observed target position at said instant is the product of the timeof projectile flight and of the velocity of said target in said computedpath, means for computing the projectile time of flight, and means toconvert the coordinates of said extrapolated point into range and anglesor' train and elevation for the projectile launching device.

8. ln an apparatus for determining the most probable position of amoving object from approximate observations of its variable coordinates,a recording device adapted to produce a record of the approximateobservations of one of said coordinates over a given time interval,filter means, input means for effectively presenting to said filtermeans the record produced by said recording device, said tilter meanshaving portions thereo't` with relatively different transmissionproperties and being adapted to respond in non-uniform fashion toditferent portions of the record presented by said input means accordingto predetermined functional relationships consistent with'the method ofleast squares, and output means responsive to the intelligencetransmitted by said tilter means and adapted to combine the varianteffects thereof according to predetermined relationships consistent withthe method of least squares for providing an output signal whichrepresents the most probable value of said one coordinate of said objectas of a selected instant.

9. In an apparatus for determining the most probable position of amoving object from approximate observations of its variable coordinates,a recording device adapted to produce a record of the approximateobservations of one of said coordinates over a given time interval,filter means comprising a plurality of lters, input means Yforeffectively presenting to each of said filters the record produced bysaid recording device, said lters having relativelydiferentetransmission properties, and atleast some of said filters beingadapted to respond in non-uniform fashion to different portions of therecord presented by said input means, all according to predeterminedrelatiopships consistent with the method of least squares, and outputmeans responsive to the intelligence transmitted by said filter meansand adapted to combine the variant effects of each filter and theoutputs of the several filters according to predetermined relationshipsconsistent with the method of least squares for providing an out-putsignal which represents the determined rate at which said one coordinateof said object is varying at a selected instamt.

i0. In an apparatus for determining the most probable position of amoving object from approximate observations of its variable coordinates,recording means adapted to produce individual records of thc approximateobservations of the respective coordinates over a given time interval,filter means, input means for effectively presenting to said filtermeans the records produced by said recording means, said filter meanscomprising a plurality of filter devices, one for each of said records,each of said filter devices having portions thereof with relativelydifferent transmission properties and being adapted to respond innon-uniform fashion to different portions of its respective input recordaccording to predetermined relationships consistent with the method ofleast squares, and output means responsive to the intelligencetransmitted by each of said iilter devices and adapted to cornbine thevariant effects thereof according to predetermined relationshipsconsistent with the method of least squares for providing outputvoltages that respectively represent the determined rates at which thecoordinates of said object are varying at a selected instant.

l1. In an apparatus for determining the most probable position of amoving object as of a given time from apa records, each of said iilterdevices having portions thereof with relatively different transmissionproperties and being adapted to respond in non-uniform fashion todifferent portions of its respective input record according topredetermined, relationships consistent with the method of Ileastsquares, and output means responsive to the intelligence transmitted byeach of said lter devices and adapted to combine the variant effectsthereof according to predetermined relationships consistent with themethod of least squares for providing output voltages that respectivelyrepresent the most probable coordinates of said object at a selectedinstant.

12. In an apparatus for `determining the most probable value of avariable from approximate observations thereof over a given timeinterval, a record medium, a recording device movable relative to saidmedium for graphically recording thereon the approximate observations ofsaid variable in spaced relationship, function filter means for derivingfrom the record on said medium a predetermined interval function of therecorded values, and means for limiting at both extremities thereof theportion of said record which is electively presented to said functioniilter means.

13. In an apparatus for determining the most probable position of amoving object from approximate observations of its variable coordinatesover a given time interval, a record medium, a recording device movablerelative to said medium for graphically recording thereon theapproximate observations of at least one of said coordinates in spacedrelationship, function filter means for deriving from the record on saidmedium a predetermined integral function of the recorded valuesaccording to the method of Ileast squares, and means for limiting atboth extremities thereof the portion of said record which is effectivelypresented to said function filter means.

References Cited in the le ofV this patent UNITED STATES PATENTS 2,43,.178 Rajchman Feb. 17, 1948 2,442,383 Stewart lune l, 1948 FOREIGNPATENTS 597,026 GreatBritain Jan. 16, 1948 634,862 Germany Sept. 5',i936

